## Monday, April 16, 2018

### A Book of Chocolates

I’ve enjoyed every David Wells’ math book I’ve ever encountered so didn’t hesitate, for \$1, snapping up a 20+ year-old volume by him I saw at a recent used book sale, “The Penguin Book of Curious and Interesting Mathematics” —  260+ pages of fun, entertaining mathematical anecdotes, factoids, quotations, curiosities/tidbits.
I’d heartily recommend this volume to any math-lovers. It’s a veritable big box-of-chocolates for the math fan!

Here’s one simple morsel (I've re-written) from early in the book, just an old Paul ErdÃ¶s puzzle:

Prove that if you have n + 1 positive integers all of which are less than or equal to 2n, then at least one pair of them are relatively prime.
.
.
.
.
.
.
.
.
.
.
.

. there are several ways to prove it, but one logical way is simply to realize that having n+1 integers less than or equal to 2n necessarily entails at least two of the integers being consecutive, and therefore relatively prime (...for n integers less than or equal to 2n this would no longer hold for ANY set of even integers).

[I'll probably offer a few more bits from the volume through this week.]